No multiple of 10

[RaquelM116]

I saw an answer for a Math problem but I'm not sure it is correct.

Here is the path where the problem is: GMAT Student Center > Homework & Pactice > Challenge Problems > Problem Title "No multiples of 10"

The problem states: If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both pand q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.
(2) q is not a multiple of 10.

In the answer is written:
"The question stem can be translated and simplified as follows:
N*(100-p / 100)*(100+q / 100) = N
(100-p / 100)*(100+q / 100) = 1
(100-p)*(100+q) = 10,000"

My concern is that if N equals to zero, which is a possibility since the statement didn't say N is not zero, so one should not divide N by N resulting 1. Then the correct answer is "E".

Please, let me know if my reasoning is correct or if I'm making a mistake.

[RonPurewal]

ok, see, you're looking for 'tricks' here.

i suppose you are technically correct (and that the word 'nonzero' should be inserted into the problem statement at some point).

HOWEVER...
if you are thinking like this, then...
...at best you are totally wasting your time,
...or, worse, you might get the incorrect answer to a problem you fully understand.

--

please know the following things about this exam, right from the start:
• there are NO 'trick questions' on this exam, EVER.
• if you think of 'tricky' cases, IGNORE THEM.
end of story.

i wrote about this here:
https://www.manhattanprep.com/gmat/foru ... ml#p116154

[RonPurewal]

okay, check out...
DS #71 in the 13th/2015 OG,
or
DS #89 in the 2016 OG.
(these are the same problem, so you only need to look in one book.)

if you do exactly what you did here, then you will get the wrong answer to that problem as a result.

...so, if you ever find your brain scavenging the ground for 'tricks' again, please remember that problem. (and, if you've ever had the displeasure of hearing my voice, imagine me saying "DON'T DO IT".)

[RonPurewal]

also, that problem has existed since the 12th edition of the OG (that's 3 revisions ago), and, in all that time, GMAT has not bothered to add the 'nonzero' caveat. so, that should tell you something about the mentality that test takers are expected to have.

this should all make perfect sense if you just think for a moment about the ultimate purpose of this exam. if this exam featured 'trick' questions, it would be totally useless to business schools.

in fact, it's worse—the inclusion of 'trick' questions would almost certainly bias the test AGAINST the best candidates.



(the LSAT, by contrast, DOES contain a fair number of 'tricky' problems... but that too should make perfect sense, since "aha! i found this tricky loophole!" figures significantly in the work of lawyers.)

[RaquelM116]

Hi Ron, thanks for your explanation.
However, I was not looking for any tricks. I was actually trying to solve considering math accuracy pertinent to any math problem. If we are in PS field, I might agree with you since the test makers will provide only one possible correct choice. In this way, being N a nonzero number is a test makers' onus. But in this DS problem, I can find 2 accurate choices depending on what I'm assuming. And I will be assuming because the statement only says N is a number, so I can consider it cannot be a zero or it can. I saw the problem you suggested (#71 OG 13/15) but in that case is logic to assume n is not zero. "n" can be neither negative nor non-integer, because n is a number of people. From the 1st statement ("The first n people donated 1/16 of the total amount donated") I know that n is nonzero, because there is an amount donated so someone donated it. In the second statement, "The total amount donated is $120000" is the same reasoning. If there is an amount donated by someone, n is not zero.
I understand that I should not look for tricks, but I should definitely not mistake a math rule such as "Do not divide by zero".
Can you tell me what is the number of this question on OG12, please? I would like to see the explanation
I really think the more accurate answer for this No multiple of 10 problem is E.
Tkank you again.

[RonPurewal]

the OG 12 problem is the same as the one in the other OG's. it's the same problem i cited above.

[RonPurewal]

also—
in fact, this whole thing is a non-issue here anyway, because zero IS a multiple of 10.
in fact, zero is a multiple of EVERY integer.
so, your objection is in fact a non-objection, because zero does not satisfy either of the statements. the answer is unaffected.

(...but, again, this is the sort of thing that will never be tested on the exam.)